信念修正逻辑初探
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摘要
经典的信念逻辑系统S_(KD45)只能表达主体某个静止状态的信念及推理,事实上,在收到新信息后,主体的信念将发生变化。动态认知逻辑是动态逻辑和认知逻辑相结合的结果,它为信息变化提供了一种形式化的处理方法。本文旨在建立一个能处理信念变化的信念修正逻辑系统S_(DBR)。
第一部分:首先介绍经典的信念逻辑系统S_(KD45),该系统能较好地刻画相信算子的性质:无矛盾性、正内省性、负内省性,同时指出它的不足——不能描述动作所产生的变化,也不能刻画多主体间的相互作用。接着介绍传统的信念修正理论——AGM理论,它虽然能反映主体信念变化的过程,但并不是一个形式化的系统。
第二部分:为了将信念排序,首先介绍顺序条件函数,它可以处理当主体收到带一定牢固度的命题后信念是如何变化的。在此基础上,引入静态的信念逻辑系统S_(SBR),给出语言、语义以及证明系统,最后给出完备性的证明。
第三部分:在静态的信念逻辑系统S_(SBR)基础上,将行动模型在认知逻辑中的执行作为动态模态算子引入逻辑语言中,建立动态的信念修正逻辑系统S_(DBR)。由于S_(DBR)可以归约到S_(SBR),所以可以证明S_(DBR)也是完备的。
第四部分:对S_(DBR)做出评价,指出不足之处,并指明在未来需要进一步研究的问题。
The classical system of doxastic logic------S_(KD45), can model agent's belief and reasoningonly in some static states. In fact, after receiving a new piece of information to the belief set, the epistemic agent will change old belief set. Dynamic epistemic logic(DEL), which merges dynamic logic and epistemic logic, provides formal means of analysis of information change.In this thesis, a logic system will be proposed------dynamic logic of belief revision(DBR),which can model belief change .
Part one: As a classical system------S_(KD45). it is successful to express strongly the properties of belief: weaker knowledge; positive introspection; negative positive introspection. At the same time, it's false to treat the change and interaction of multi-agent. Sequentially, although belief revision theory conceived by C.Alchourron, P.Gardenfors and D.Mackinson(AGM) treat the change successfully, it is not yet a formal system.
Part two: An ordinal conditional function(OCF) expresses a ranking of propositions, and it represents agent's revised belief after receiving a piece of information with firmness a. On the base of OCF, this paper introduces a static logic of belief revision (SBR), including syntax, semantics and proof system. Finally, the logic system is proved complete.
Part three: After extending the SBR, by introducing the execution of the action model in epistemic model as a dynamic operator into the logical language, this paper sets up a dynamic logic of belief revision (DBR). It is can be proved that the DBR also is reduced to the SBR, so DBR system is complete too.
Part four: I comment on the DBR, and give some problems for further research in the future.
第一部分:首先介绍经典的信念逻辑系统S_(KD45),该系统能较好地刻画相信算子的性质:无矛盾性、正内省性、负内省性,同时指出它的不足——不能描述动作所产生的变化,也不能刻画多主体间的相互作用。接着介绍传统的信念修正理论——AGM理论,它虽然能反映主体信念变化的过程,但并不是一个形式化的系统。
第二部分:为了将信念排序,首先介绍顺序条件函数,它可以处理当主体收到带一定牢固度的命题后信念是如何变化的。在此基础上,引入静态的信念逻辑系统S_(SBR),给出语言、语义以及证明系统,最后给出完备性的证明。
第三部分:在静态的信念逻辑系统S_(SBR)基础上,将行动模型在认知逻辑中的执行作为动态模态算子引入逻辑语言中,建立动态的信念修正逻辑系统S_(DBR)。由于S_(DBR)可以归约到S_(SBR),所以可以证明S_(DBR)也是完备的。
第四部分:对S_(DBR)做出评价,指出不足之处,并指明在未来需要进一步研究的问题。
The classical system of doxastic logic------S_(KD45), can model agent's belief and reasoningonly in some static states. In fact, after receiving a new piece of information to the belief set, the epistemic agent will change old belief set. Dynamic epistemic logic(DEL), which merges dynamic logic and epistemic logic, provides formal means of analysis of information change.In this thesis, a logic system will be proposed------dynamic logic of belief revision(DBR),which can model belief change .
Part one: As a classical system------S_(KD45). it is successful to express strongly the properties of belief: weaker knowledge; positive introspection; negative positive introspection. At the same time, it's false to treat the change and interaction of multi-agent. Sequentially, although belief revision theory conceived by C.Alchourron, P.Gardenfors and D.Mackinson(AGM) treat the change successfully, it is not yet a formal system.
Part two: An ordinal conditional function(OCF) expresses a ranking of propositions, and it represents agent's revised belief after receiving a piece of information with firmness a. On the base of OCF, this paper introduces a static logic of belief revision (SBR), including syntax, semantics and proof system. Finally, the logic system is proved complete.
Part three: After extending the SBR, by introducing the execution of the action model in epistemic model as a dynamic operator into the logical language, this paper sets up a dynamic logic of belief revision (DBR). It is can be proved that the DBR also is reduced to the SBR, so DBR system is complete too.
Part four: I comment on the DBR, and give some problems for further research in the future.
引文
7 C.E.Alchourron,P.Gardenfors and D.Makinson.On the Logic of Theory Change:Partial Meet Contraction and Revision Functions[J].Journal of Symbolic Logic,50:510-530,1985.
8 Hans van Ditmarsch.Belief change and dynamic logic[A].In:J.Delgrande and J.Lang and H.Rott and J.-M.Tallon(eds.),Belief Change in Rational Agents:Perspectives from Artificial Intelligence,Philosophy,and Economics[C],2005.
9 J.van Benthem.Dynamic logic for beliefrevision[J].Journal of Applied Non-Classical Logic,2007(17),1-27.
10 G.Aucher.A Combined System for Update Logic and Belief Revision.Master's thesis,ILLC,University of Amsterdam,2003.
11 H.J.Levesque.A logic of Implict and Explicit Belief[A].Proceedings of the National Conference on Artificial Intelligence[C],1984,198-202.
12 周昌乐.认知逻辑导论[M].清华大学出版社,广西科学技术出版社出版,2001,p121.
17K⊥表示信念集不一致。
18 C.E.Alchourron,P.Gardenfors and D.Makinson.On the Logic of Theory Change:Partial Meet Contraction and Revision Functions[J].Journal of Symbolic Logic,50:510-530,1985.
19P.Gardenfors,D.Makinson.Revision of Knowledge Systems:Using Epistemic Entrenchment[A].Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge[C].83-95,1988.
20B.Nebel.Base revision operations and schemes:Semantics,representation,and complexity[A].In:Cohn A G eds,Proceedings of 11th European Conference on Artificial Intelligence[C].1994.
21M.Dalal.Investigations into a theory of knowledge base revision:Preliminary report[A].In:Proceedings of the 7th National Conference on AI[C].1988,475-479.
22B.Nebel.Base revision operations and schemes:Semantics,representation,and complexity[A].In:Cohn A G eds, Proceedings of 11th European Conference on Artificial Intelligence[C],1994.
23B.Malheiro,O.Euganio.Argumentation as distributed belief revision:Conflict resolution in decentralized co-operative multi-agent systems[A].In:Proceedings of the 10th Portuguese Conference on Artificial Intelligence[C].Porto,Portugal,205-218,2001.
[1]P.Gardenfors.Knowledge in Flux[M].The MIT Press,Cambridge(Mass.),1987.
[2]B.F.Chellas.Modal Logic[M].Cambridge,U.K.,Cambridge University Press,1980.
[3]A.Baltag,L.S.Moss,S.Solecki.The Logic of Common Knowledge,Public Announcements,and Private Suspicions.GILBOA I.,Ed.,Proceedings of the 7~(th)Conference on Theoretical Aspects of Rationality and Knowledge(TARK98),1998.
[4]P.Gardenfors.Knowledge in Flux:Modeling the Dynamics of Epistemic States[M].Cambridge,The MIT Press,1988.
[5]S.Kraus,D.Lehmann.Knowledge,Belief and Time[A].In:L.Kott ed.Proceedings of the 13~(th)Int.Colloquium on Automata,Languages and Programming[C],Rennes,LNCS226,Berlin:Springer,1986.
[6]G.Aucher.A Combined System for Update Logic and Belief Revision.Master's thesis,ILLC,University of Amsterdam,2003.
[7]G.Aucher.How our beliefs contribute to interpret actions[A].In L.Z.Varga.pechoucek,P.petta,editor,CEEMAS2005[C].276-286.Springer,2005.LNAI3690.
[8]F.Liu.Dynamic variations:Update and revision for diverse agents.Master's thesis,ILLC,University of Amsterdam,2004.
[9]C.E.Alchourron,P.Gardenfors and D.Makinson.On the Logic of Theory Change:Partial Meet Contraction and Revision Functions[J].Journal of Symbolic Logic,50:510-530,1985.
[10]A.Grove.Two Modellings for Theory Change[J].Journal of Philosophical Logic,17:157-170,1988.
[11]P.Gardenfors.Belief Revision:An Introduction[A].In:P.Gardenfors,ed.Belief Revision[C].Cambridge University Press,1992,1-28.
[12]F.Liu.Diversity of agents and Interaction.Tech Report,ILLC,University of Amsterdam,2007.
[13]W.Spohn.Ordinal conditional functions -a dynamic theory of epistemic states[EB/OL].http://citeseer.nj.nec.com/contex/4500/0.
[14]J.Van Benthem.Dynamic logic for belief revision[J].Journal of Applied Non-Classical Logic,2007(17),1-27.
[15]周昌乐.认知逻辑导论[M].清华大学出版社,广西科学技术出版社,2001.
[16]弓肇祥.认知逻辑新发展[M].北京大学出版社,北京,2004.
[17]唐晓嘉.认知的逻辑分析[M].西南师范大学出版社,重庆,2003.
[18]周北海.模态逻辑[M].北京大学出版社,第1版,北京,1996.
[19]郭美云.带群体知识的动态认知逻辑[D].北京大学,北京,2006.
[20]刘瑞胜.认识逻辑(1):关于知识和信念的逻辑框架[J].计算机学报,1998(7),627-637
[21]刘虎,鞠实儿.信念逻辑的逻辑全知问题[J].求是学刊,2007(6),31-34.
[22]郭佳宏.信念变化的逻辑[J].求是学刊,2007(6),34-38.
[23]熊立文.信念修正的AGM理论[J].现代哲学,2005(1),127-131.
8 Hans van Ditmarsch.Belief change and dynamic logic[A].In:J.Delgrande and J.Lang and H.Rott and J.-M.Tallon(eds.),Belief Change in Rational Agents:Perspectives from Artificial Intelligence,Philosophy,and Economics[C],2005.
9 J.van Benthem.Dynamic logic for beliefrevision[J].Journal of Applied Non-Classical Logic,2007(17),1-27.
10 G.Aucher.A Combined System for Update Logic and Belief Revision.Master's thesis,ILLC,University of Amsterdam,2003.
11 H.J.Levesque.A logic of Implict and Explicit Belief[A].Proceedings of the National Conference on Artificial Intelligence[C],1984,198-202.
12 周昌乐.认知逻辑导论[M].清华大学出版社,广西科学技术出版社出版,2001,p121.
17K⊥表示信念集不一致。
18 C.E.Alchourron,P.Gardenfors and D.Makinson.On the Logic of Theory Change:Partial Meet Contraction and Revision Functions[J].Journal of Symbolic Logic,50:510-530,1985.
19P.Gardenfors,D.Makinson.Revision of Knowledge Systems:Using Epistemic Entrenchment[A].Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge[C].83-95,1988.
20B.Nebel.Base revision operations and schemes:Semantics,representation,and complexity[A].In:Cohn A G eds,Proceedings of 11th European Conference on Artificial Intelligence[C].1994.
21M.Dalal.Investigations into a theory of knowledge base revision:Preliminary report[A].In:Proceedings of the 7th National Conference on AI[C].1988,475-479.
22B.Nebel.Base revision operations and schemes:Semantics,representation,and complexity[A].In:Cohn A G eds, Proceedings of 11th European Conference on Artificial Intelligence[C],1994.
23B.Malheiro,O.Euganio.Argumentation as distributed belief revision:Conflict resolution in decentralized co-operative multi-agent systems[A].In:Proceedings of the 10th Portuguese Conference on Artificial Intelligence[C].Porto,Portugal,205-218,2001.
[1]P.Gardenfors.Knowledge in Flux[M].The MIT Press,Cambridge(Mass.),1987.
[2]B.F.Chellas.Modal Logic[M].Cambridge,U.K.,Cambridge University Press,1980.
[3]A.Baltag,L.S.Moss,S.Solecki.The Logic of Common Knowledge,Public Announcements,and Private Suspicions.GILBOA I.,Ed.,Proceedings of the 7~(th)Conference on Theoretical Aspects of Rationality and Knowledge(TARK98),1998.
[4]P.Gardenfors.Knowledge in Flux:Modeling the Dynamics of Epistemic States[M].Cambridge,The MIT Press,1988.
[5]S.Kraus,D.Lehmann.Knowledge,Belief and Time[A].In:L.Kott ed.Proceedings of the 13~(th)Int.Colloquium on Automata,Languages and Programming[C],Rennes,LNCS226,Berlin:Springer,1986.
[6]G.Aucher.A Combined System for Update Logic and Belief Revision.Master's thesis,ILLC,University of Amsterdam,2003.
[7]G.Aucher.How our beliefs contribute to interpret actions[A].In L.Z.Varga.pechoucek,P.petta,editor,CEEMAS2005[C].276-286.Springer,2005.LNAI3690.
[8]F.Liu.Dynamic variations:Update and revision for diverse agents.Master's thesis,ILLC,University of Amsterdam,2004.
[9]C.E.Alchourron,P.Gardenfors and D.Makinson.On the Logic of Theory Change:Partial Meet Contraction and Revision Functions[J].Journal of Symbolic Logic,50:510-530,1985.
[10]A.Grove.Two Modellings for Theory Change[J].Journal of Philosophical Logic,17:157-170,1988.
[11]P.Gardenfors.Belief Revision:An Introduction[A].In:P.Gardenfors,ed.Belief Revision[C].Cambridge University Press,1992,1-28.
[12]F.Liu.Diversity of agents and Interaction.Tech Report,ILLC,University of Amsterdam,2007.
[13]W.Spohn.Ordinal conditional functions -a dynamic theory of epistemic states[EB/OL].http://citeseer.nj.nec.com/contex/4500/0.
[14]J.Van Benthem.Dynamic logic for belief revision[J].Journal of Applied Non-Classical Logic,2007(17),1-27.
[15]周昌乐.认知逻辑导论[M].清华大学出版社,广西科学技术出版社,2001.
[16]弓肇祥.认知逻辑新发展[M].北京大学出版社,北京,2004.
[17]唐晓嘉.认知的逻辑分析[M].西南师范大学出版社,重庆,2003.
[18]周北海.模态逻辑[M].北京大学出版社,第1版,北京,1996.
[19]郭美云.带群体知识的动态认知逻辑[D].北京大学,北京,2006.
[20]刘瑞胜.认识逻辑(1):关于知识和信念的逻辑框架[J].计算机学报,1998(7),627-637
[21]刘虎,鞠实儿.信念逻辑的逻辑全知问题[J].求是学刊,2007(6),31-34.
[22]郭佳宏.信念变化的逻辑[J].求是学刊,2007(6),34-38.
[23]熊立文.信念修正的AGM理论[J].现代哲学,2005(1),127-131.